On temporal characteristics in an exponential queueing system with negative claims and a bunker for ousted claims

We consider a queueing system with Poisson input streams of positive and negative claims, an infinite collector, and exponential service. A negative claim ousts a positive claim out of the collector queue and moves it to a bunker of unbounded capacity. If the collector is empty then a negative claim leaves the system with no influence on it. After a claim is serviced, the device receives the next claim from the collector or, if the collector is empty, from the bunker. For different combinations of $FIFO$ and $LIFO$ orders of choosing a claim for service from the collector's queue, choosing a claim for service from the bunker's queue, and ousting claims from the collector to the bunker, we obtain formulas for computing the stationary waiting time distribution for a claim to begin service and other temporal characteristics.

Presented by the member of Editorial Board: A. I. Lyakhov